The invention relates to the field of solid-state based electro-magnetically induced transparency (EIT), and in particular to exploring solid-state-based electro-magnetically induced transparency (EIT) as a non-linear medium in photonic crystal cavities.
In the nodes of any long-haul telecommunication network, one needs to perform electro-optical conversion in order to process optical signals. The tasks that typically need to be performed include: routing, regeneration, changing wavelengths, changing bit-rates, etc. Since bit-rates in long-haul networks are typically high (10 Gbit/s today, and 40 Gbit/s in the next generation networks), one is forced to use ultra-fast (>100 GHz for 40 Gbit/s) electronics to perform such tasks. There are various physical reasons that prevent electronics from functioning well at so high frequencies, making such electronics extremely expensive. In fact, almost 90% of the cost of any long-haul network lies in modules that perform electro-optical conversion. Consequently, there is a rapidly growing need and interest in developing satisfactory all-optical signal processing. The requirements on all-optical signal processing are: to be ultra-fast (>100 GHz) and operate at telecommunication power levels (<5 mW peak power). Furthermore, it would be highly beneficial if the all-optical solution would be integrable (and therefore small); integrating many functions on the same chip would drastically reduce production and operating costs. Unfortunately, in experimental integrated all-optical devices that achieve the desired performance today, much higher power levels are needed.
Another important application where very large optical non-linearities could play a crucial role is the emerging field of quantum information, and quantum computation. Due to their minimal interactions with environment (so decoherence rates are low), and low absorption losses in many media, photons are the preferred long-distance carriers of quantum information. At various nodes of such a quantum-information network, the information will need to be processed. Although quantum information can be transferred from one system (e.g. photons) into another (e.g. electrons), and then back, such transfers are technologically challenging. Consequently, there is a need to perform all-optical quantum-information processing. To achieve this, one has to have non-linear effects large enough to be triggered by single-photon power levels. More generally, because of their low decoherence rates, photons might very well also turn out to be the preferred way of implementing quantum computation. In that case, the currently non-existing capability to influence the quantum state of a single photon with a single other photon will become even more important.
In early 1980s, the prospect of all-optical computers was a hot area of research. Such computers could conceivably operate at much higher clock speeds, and would be much more amenable to high-degree parallelization than electronic computers. Unfortunately, the power requirements needed to obtain large enough non-linearities to realize this scheme with the solutions that existed at the time were many orders of magnitude too large for all-optical computing to be feasible. For example, even using the most optimistic currently available technology and ultra-fast materials, an all-optical logical gate operating at 10 Gbit/s would require operational power >1 mW. If one imagines a 1 cm*1 cm surface all-optical microprocessor with 106 such gates, which is a typical number of gates needed for very large-scale integration (VLSI), one needs to supply 1 kW to such a microprocessor, and at the same time be able to remove all the heat generated when operating with such large powers. Clearly, this scheme is not feasible. Nevertheless, it seems that if better non-linear materials were available so that the needed power is reduced by say 3 orders of magnitude, all-optical computing would become a very interesting prospect again.
One approach to achieve enhancement of non-linear effects is to find materials that have as strong non-linear responses as possible. One can obtain fairly large non-linear effects with only moderate power levels if one is willing to use materials with slow time responses. In such materials, the non-linear effect is basically cumulative in time, so many photons participate over time in establishing the given non-linear effect: the longer the accumulation time, the lower the power requirements. Unfortunately, this approach cannot be used if ultra-fast operation is desired. In fact, the only non-linearities at our disposal that have a response and recovery time faster than 1 ns are based either on electronic polarization, or on molecular orientation; for response times faster than 1 ps, the only viable option is exploring non-linear effects based on electronic-polarization.
In simplified terms, non-linear effects based on electronic-polarization come about because a strong external electrical field modifies the electronic orbit to the point where the polarization becomes non-linear in the applied field. Clearly, the scale that sets the onset of this non-linear behavior is given by the electrical field that binds the electron to the atom; consequently, large external field intensities are required to observe non-linear behavior. Consider, for example, the Kerr effect in which the non-linearly induced change to the index of refraction is given by δn=n2*I, where I is the intensity; for GaAs at λAIR=1.55 μm, n2=1.5*10−13 cm2/W, and to obtain δn=10−4, I=1 GW/cm2 is needed. These requirements can be somewhat lowered if the electrons are only weakly bound, like for example in some polymers (which have large orbitals), or in quantum dots. Still, improvements of more than one order of magnitude are un-feasible, and such materials are typically difficult to work with and difficult to integrate with other optical materials on the same chip.
In principle, huge non-linear responses could be obtained, if the carrier frequency of the optical beam is close to an electronic transition resonance frequency; in that case, even a small applied intensity can significantly distort the electronic-orbit, and drive it into the non-linear regime. Unfortunately, this approach is necessarily accompanied with enormously large absorption of the optical beam. Furthermore, since this is a resonant phenomenon, the response and recovery times are necessarily large. Nevertheless, under certain conditions, one can apply another (coupling) frequency beam whose presence (through quantum interference) prevents the absorption of the original (probe) beam, like in FIG. 1A; this is the essence of the phenomenon of electro-magnetically induced transparency (EIT).
FIG. 1A is schematic diagram of an EIT system 2, which involves 3 states |1>, |2>, and |3>; the system is initially in state |1>. A probe beam 4, with frequency ωp is resonant with the transition |1>→|3>; if this is the only beam present, it experiences large absorption. However, another (coupling) beam 6 can be applied, with frequency ωc, being resonant with the transition |2>→|3>, so the electro-magnetically induced transparency (EIT) makes the medium transparent to ωp. FIGS. 1B–1C show results of an EIT experiment. FIG. 1B shows transmission as a function of ωp (when ωc is present); FIG. 1C shows the refractive index as observed by ωp as a function of ωp. EIT has been demonstrated to reduce absorptions of the probe beams by numerous orders of magnitude in many different systems.
Since in EIT the probe beam frequency is at the peak of an electronic resonance transition, the non-linear response is enormous. For example, measured Kerr coefficient as large as n2=0.18 cm2/W, are obtainable, which is 12 orders of magnitude larger than the Kerr coefficient of GaAs. With currently existing experimental setups, such a large Kerr coefficient is already close to enabling non-linear effects at single-photon levels. Furthermore, the response and recovery times for such large non-linearities can be made to be faster than 1 ps.
Another approach of maximizing non-linear effects has to do with optimizing the structure of the device (rather than the material). A simple way to make use of the tiny non-linear effects that result when modest intensity beams propagate in a typical material is to allow the effects to accumulate over long propagation distance. This approach has been successfully used for many applications, but typically imposes some serious constraints. For example, in order to accumulate non-linearly self-induced phase shift of π (which can then be explored for interferometric switching) with a 5 mW peak-power signal in a typical silica fiber (λAIR=1.55 μm, n2=3*10−16 cm2/W, modal area ≈50 μm2), one needs to propagate for more than 200 km, which is prohibitively too long given the linear losses of silica of 0.2 dB/km.
An additional approach that can be taken is to reduce the modal area. Since the non-linearities depend on the intensity, structures with smaller modal areas have smaller power requirements. Silica fibers exploit low index-contrast guiding, so their modal areas are fairly large. When a high index-contrast is used (like in integrated optics), the modal area can be readily reduced to <(λ/3)2, which decreases the length requirements by almost three orders of magnitude compared with silica fibers. Also, silica is a particularly bad non-linear material; materials used in integrated optics typically have Kerr coefficients almost three orders of magnitude larger than silica. Putting both of these facts together, one needs to propagate a 5 mW peak power signal for ≈1 m in order to achieve self-induced non-linear phase shift of π, 1 m is clearly way too long to be used in integrated optics.
An additional mechanism that can be explored to boost non-linear effects is to use waveguides with small group velocity; it has been shown that for a fixed power, the length requirements are proportional to (νG/c)2, where νG is the group velocity of the signal in the waveguide. Using a GaAs waveguide with νG=c/100, modal area (λ/3)2, and 5 mW peak-power signals, a self-induced non-linear phase shift of π can be obtained after a propagation distance of ≈1 mm.